A distribution-free multivariate CUSUM control chart using dynamic control limits

In modern quality control, it is becoming common to simultaneously monitor several quality characteristics of a process with rapid evolving data-acquisition technology. When the multivariate process distribution is unknown and only a set of in-control data is available, the bootstrap technique can be used to adjust the constant limit of the multivariate cumulative sum (MCUSUM) control chart. To further improve the performance of the control chart, we extend the constant control limit to a sequence of dynamic control limits which are determined by the conditional distribution of the charting statistics given the sprint length. Simulation results show that the novel control chart with dynamic control limits offers a better ARL performance, compared with the traditional MCUSUM control chart. Despite it, the proposed control chart is considerably computer-intensive. This leads to the development of a more flexible control chart which uses a continuous function of the sprint length as the control limit sequences. More importantly, the control chart is easy to implement and can reduce the computational time significantly. A white wine data illustrates that the novel control chart performs quite well in applications.